Camera rotates around object at awkward angle
To fix this, I applied a camera actuator to the camera instead of parenting the camera to the car. The camera actuator allows the camera to track an object and choose how precisely it tracks it using damping (e.g. if the car goes over a pothole it won't shake the camera, but if it goes over a big hill, the camera will follow it). Here is a picture of the actuator settings:



You can learn more about camera actuators here.